Answer:
[tex]\displaystyle y'' = \frac{-1}{\ln(10)x^2}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \log (x)[/tex]
Step 2: Differentiate
- Logarithmic Differentiation: [tex]\displaystyle y' = \frac{1}{\ln(10)x}[/tex]
- Derivative Property [Multiplied Constant]: [tex]\displaystyle y'' = \frac{1}{\ln 10} \frac{d}{dx} \bigg[ \frac{1}{x} \bigg][/tex]
- Basic Power Rule: [tex]\displaystyle y'' = \frac{-1}{\ln(10)x^2}[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
